Combining the contact model of elastic-layered solid with the concept of asperity contact in elastohydrodynamic lubrication (EHL), a mixed-lubrication model is presented to predict friction coefficient over rough surfaces with/without an elastic-layered medium under entire lubrication regimes. Solution of contact problems for elastic-layered solids is presented based upon the classical model of Greenwood and Williamson (GW) in conjunction with Chen and Engel's analysis. The effects of the Young's modulus ratio of the layer to substrate and the thickness of the layer on the elastic real area of contact and contact load for a fixed dimensionless separation are studied using the proposed method, which is used for the asperities having contact with an elastic coating. Coefficient of friction with elastic-layered solids in boundary lubrication is calculated in terms of Rabinowicz's findings and elastic-layered solutions of Gupta and Walowit. The effect of rough contacts with an elastic layer on friction coefficient in lubrication regimes has been analyzed. Variations in plasticity index significantly affect friction coefficients in boundary and mixed lubrications. For a large value of , the degree of plastic contact exhibits a stronger dependence of the mean separation or film thickness than the roughness, and for a small value of , the opposite result is true. The effect of governing parameters, such as inlet oil viscosity at ambient pressure, pressure–viscosity coefficient, combined surface roughness, and on friction coefficient, has been investigated. Simulations are shown to be in good agreement with the experimental friction data.